The Implicit Function Theorem : History, Theory, and Applications / by Steven G. Krantz, Harold R. Parks
(Modern Birkhäuser Classics)
| データ種別 | 電子ブック |
|---|---|
| 出版情報 | New York, NY : Springer New York : Imprint: Birkhäuser , 2013 |
| 本文言語 | 英語 |
| 大きさ | XIII, 163 p : online resource |
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| 内容注記 | Preface Introduction to the Implicit Function Theorem History Basic Ideas Applications Variations and Generalizations Advanced Implicit Function Theorems Glossary Bibliography Index |
|---|---|
| 一般注記 | The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth functions, and (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash–Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present uncorrected reprint of this classic monograph. Originally published in 2002, The Implicit Function Theorem is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas |
| 著者標目 | *Krantz, Steven G. author Parks, Harold R. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Mathematical analysis LCSH:Analysis (Mathematics) LCSH:Differential equations LCSH:Partial differential equations LCSH:Differential geometry LCSH:History FREE:Mathematics FREE:Analysis FREE:Partial Differential Equations FREE:Differential Geometry FREE:History of Mathematical Sciences FREE:Ordinary Differential Equations |
| 分 類 | DC23:515 |
| 巻冊次 | ISBN:9781461459811 
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| ISBN | 9781461459811 |
| URL | http://dx.doi.org/10.1007/978-1-4614-5981-1 |
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